Percent Error Formula: How to Calculate It With Examples

The percent error formula

You need two numbers: the experimental (measured) value and the accepted (true, theoretical or reference) value. Subtract, take the size of the difference, divide by the accepted value, and multiply by 100.

percent error = |experimental − accepted| ÷ |accepted| × 100The vertical bars mean absolute value, so the result is never negative.

Some courses keep the sign and write (experimental − accepted) ÷ accepted × 100. A positive result then means you overshot, and a negative one means you undershot. Check which version your instructor or textbook expects. The size of the answer is the same either way.

Worked example: measuring gravity

A student drops an object and measures an acceleration of 9.6 m/s². A commonly used accepted value for gravitational acceleration at Earth's surface is 9.81 m/s².

1. Find the difference: 9.6 − 9.81 = −0.21, whose absolute value is 0.21.
2. Divide by the accepted value: 0.21 ÷ 9.81 ≈ 0.0214.
3. Multiply by 100: the percent error is about 2.14%.

With the signed version, the answer is −2.14%, showing the measurement was a little low. The unit (m/s²) cancels out, so percent error is a pure percentage. That also means you must use the same unit for both values before you start.

Percent error vs percent difference

Percent error needs a trusted reference value. When you are comparing two measurements and neither is the "correct" one, use percent difference instead. It divides by the average of the two values, so the answer is the same whichever you list first.

percent difference = |a − b| ÷ ((a + b) ÷ 2) × 100

Worked example: two scales read 48 g and 52 g for the same object. The difference is 4, the average is 50, and 4 ÷ 50 × 100 = 8%. If you treated 50 as an accepted value for a reading of 48, you would instead get |48 − 50| ÷ 50 × 100 = 4%, a different question with a different answer.

Common mistakes

• Dividing by the measured value. The denominator is the accepted value. Dividing by your own result changes the answer, here giving 0.21 ÷ 9.6 = 2.19% instead of 2.14%.
• Mixing units. Convert both values to the same unit first, such as grams with grams or metres with metres.
• Rounding too early. Keep extra digits through the division and round only the final percentage.
• Using a zero accepted value. Percent error is undefined when the accepted value is 0, because you cannot divide by zero. Report the absolute error instead.
• Confusing it with percent change. A thermometer reading is compared with a reference, not with its own earlier reading.

How to interpret a percent error

A smaller percent error means the measurement is closer to the accepted value, but there is no single cut-off that counts as good. A few percent may be impressive for a school experiment with simple equipment, while a precision instrument may be expected to do far better. The acceptable size depends on the method, the equipment and the purpose.

Percent error also does not tell you the cause. A consistent error in one direction often points to a systematic issue, such as a miscalibrated instrument or a neglected factor like air resistance. Scattered errors in both directions usually come from random variation in reading or timing.

To check your own figures, use the percent error calculator. If you are comparing a before and after value instead, the percentage calculator handles percent change.